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Two New Customized Proximal Point Algorithms Without Relaxation for Linearly Constrained Convex Optimization

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Abstract

In this paper, we propose a new customized proximal point algorithm for linearly constrained convex optimization problem, and further extend the proposed method to separable convex optimization problem. Unlike the existing customized proximal point algorithms, the proposed algorithms do not involve relaxation step, but still ensure the convergence. We obtain the particular iteration schemes and the unified variational inequality perspective. The global convergence and \({\mathcal {O}}(1/k)\)-convergence rate of the proposed methods are investigated under some mild assumptions. Numerical experiments show that compared to some state-of-the-art methods, the proposed methods are effective.

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Notes

  1. The mapping F(w) is affine with a skew-symmetric matrix, and thus it is monotone; see He and Yuan [23]

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Acknowledgements

The authors are very grateful to Doctor Wen-Xing Zhang at University of Electronic Science and Technology of China for his help on numerical experiments on image processing problems. This work was also supported by the Science and Technology on Communication Information Security Control Laboratory, Xiangtan University.

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Authors and Affiliations

  1. School of Economics and Management, Fuzhou University, Fuzhou, 350108, China

    Binqian Jiang

  2. School of Mathematics and Computer Science, Fuzhou University, Fuzhou, 350108, China

    Zheng Peng & Kangkang Deng

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  1. Binqian Jiang
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  2. Zheng Peng
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  3. Kangkang Deng
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Correspondence to Zheng Peng.

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Communicated by Majid Soleimani-damaneh.

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This work was supported by the Natural Science Foundation of China with Grants 11571074 and 11726505.

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Jiang, B., Peng, Z. & Deng, K. Two New Customized Proximal Point Algorithms Without Relaxation for Linearly Constrained Convex Optimization. Bull. Iran. Math. Soc. 46, 865–892 (2020). https://doi.org/10.1007/s41980-019-00298-0

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